Radical Equations and Extraneous Roots Answers
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1
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Do you agree? Explain why or why not.
Answer:
I do not agree with the student. While solving the equation results in x = 4, this is an extraneous solution. When you substitute 4 back into the original equation, you get sqrt(2(4) + 1) + 3 = 0, which simplifies to 3 + 3 = 0, or 6 = 0. Since this is a false statement, x = 4 is not a solution. Furthermore, the equation sqrt(2x + 1) = -3 has no real solution because a principal square root cannot be negative.
1
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Do you agree with the student? Explain why or why not.
A
I do not agree with the student because there is no real solution.
B
Checking the solutions in the original equation verifies ; however, is extraneous.C
Checking the solutions in the original equation shows that 6 is an extraneous solution.D
I agree with the student because both and satisfy the original equation.
2
Did your explanation include the following?
A
I do not agree with the student because there is no real solution.B
Solving the equation only gives possible solutions, but you must check them in the original equation.C
Checking the solution in the original equation shows that 4 is an extraneous solution.Did you find these answers helpful?
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